Unified error analysis for nonconforming space discretizations of wave-type equations

DOI10.1093/imanum/dry036zbMath1466.65135OpenAlexW2884327527MaRDI QIDQ5854353

David Hipp, Christian Stohrer, Marlis Hochbruck

Publication date: 16 March 2021

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imanum/dry036

zbMATH Keywords

wave equationisoparametric finite elementsdynamic boundary conditionsoperator semigroupslinear evolution equationsnonconforming space discretization\textit{a priori} error boundsabstract error analysislinear monotone operators in Hilbert spaces

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Hydro- and aero-acoustics (76Q05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

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Nonlinear wave equation with Dirichlet and acoustic boundary conditions: theoretical analysis and numerical simulation ⋮ Full discretization error analysis of exponential integrators for semilinear wave equations ⋮ The Heterogeneous Multiscale Method for Dispersive Maxwell Systems ⋮ Splitting schemes for the semi-linear wave equation with dynamic boundary conditions ⋮ Stability for Semilinear Wave Equation in an Inhomogeneous Medium with Frictional Localized Damping and Acoustic Boundary Conditions ⋮ Finite element discretization of semilinear acoustic wave equations with kinetic boundary conditions ⋮ On a nonlinear problem with Dirichlet and acoustic boundary conditions ⋮ An implicit-explicit time discretization scheme for second-order semilinear wave equations with application to dynamic boundary conditions ⋮ Error Analysis of Discontinuous Galerkin Discretizations of a Class of Linear Wave-type Problems ⋮ Heterogeneous Multiscale Method for Maxwell's Equations ⋮ A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions

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